Floating ice shelves that fringe the coast of Antarctica resist the flow of grounded ice into the ocean. One of the key factors governing the amount of flow resistance an ice shelf provides is the rigidity (related to viscosity) of the ice that constitutes it. Ice rigidity is highly heterogeneous and must be calibrated from spatially continuous surface observations assimilated into an ice-flow model. Realistic uncertainties in calibrated rigidity values are needed to quantify uncertainties in ice sheet and sea-level forecasts. Here, we present a physics-informed machine learning framework for inferring the full probability distribution of rigidity values for a given ice shelf, conditioned on ice surface velocity and thickness fields derived from remote-sensing data. We employ variational inference to jointly train neural networks and a variational Gaussian Process to reconstruct surface observations, rigidity values and uncertainties. Applying the framework to synthetic and large ice shelves in Antarctica demonstrates that rigidity is well-constrained where ice deformation is measurable within the noise level of the observations. Further reduction in uncertainties can be achieved by complementing variational inference with conventional inversion methods. Our results demonstrate a path forward for continuously updated calibrations of ice flow parameters from remote-sensing observations.

Understanding the dynamic behaviour of ice shelves, specifically the controls on their ability to buttress the flow of ice into the ocean, is critical for predicting future ice-sheet contributions to sea level rise. Many large ice shelves, which are predominantly composed of meteoric ice, have a basal layer of marine ice (formed from accumulated platelets at the ice–ocean interface), comprising up to 40% of their thickness locally. Differences in temperature, chemistry and microstructure between marine and meteoric ice mean the rheological properties of the ice vary throughout the ice shelf. These differences are not explicitly accounted for in ice-sheet modelling applications, and may have an important influence on ice shelf dynamics. We tested the sensitivity of a model of an idealised ice shelf to variations in temperature distribution and flow enhancement, and found that incorporating a realistic thermal profile (where the marine ice layer is isothermal) had an order of magnitude greater effect on ice mass flux and thinning than incorporating the mechanical properties of the marine ice. The presence of marine ice at the ice shelf base has the potential to significantly increase deviatoric stresses at the surface and ice mass flux across the front of an ice shelf.

We compare different ways the bulk flow nonlinearity of glacier ice can be captured in an orthotropic rheology. Specifically, we compare the unapproximated orthotropic rheology, derived from plastic potential theory, to existing approximations that assume either the nonlinear viscosity or fluidity is identical to that of Glen's isotropic flow law. We find, overall, a reasonable agreement between the three orthotropic rheologies, and with existing Dye 3 ice-core deformation tests, although assuming Glen's viscosity provides the best approximation to the unapproximated rheology. Our results therefore suggest that previous studies based on either approximation to the orthotropic rheology are on relatively safe ground in the sense that both approximations generally agree with the unapproximated rheology and experimental data. Finally, we provide the forward and inverse analytical forms of all three rheologies for use in future numerical ice-flow modelling.

The once-contiguous Ellesmere Ice Shelf, first reported in writing by European explorers in 1876, and now almost completely disintegrated, has rolling, wave-like surface topography, the origin of which we investigate using a viscous buckling instability analysis. We show that rolls can develop during a winter season (~ 100 d) if sea-ice pressure (depth-integrated horizontal stress applied to the seaward front of the Ellesmere Ice Shelf) is sufficiently large (1 MPa m) and ice thickness sufficiently low (1–10 m). Roll wavelength initially depends only on sea-ice pressure, but evolves over time depending on amplitude growth rate. This implies that a thinner ice shelf, with its faster amplitude growth rate, will have a shorter wavelength compared to a thicker ice shelf when sea-ice pressure is equal. A drawback of the viscous buckling mechanism is that roll amplitude decays once sea-ice pressure is removed. However, non-Newtonian ice rheology, where effective viscosity, and thus roll change rate, depends on total applied stress may constrain roll decay rate to be much slower than growth rate and allow roll persistence from year to year. Whether the viscous-buckling mechanism we explore here ultimately can be confirmed as the origin of the Ellesmere Ice Shelf rolls remains for future research.

We investigate the errors caused by neglecting the crystal-orientation fabric when inferring the basal friction coefficient field, and whether such errors can be alleviated by inferring an isotropic enhancement factor field to compensate for missing fabric information. We calculate the steady states that arise from ice flowing over a sticky spot and a bedrock bump using a vertical-slab numerical ice-flow model, consisting of a Weertman sliding law and the anisotropic Johnson flow law, coupled to a spectral fabric model of lattice rotation and dynamic recrystallisation. Given the steady or transient states as input for a canonical adjoint-based inversion, we find that Glen's isotropic flow law cannot necessarily be used to infer the true basal drag or friction coefficient field, which are obscured by the orientation fabric, thus potentially affecting vertically integrated mass fluxes. By inverting for an equivalent isotropic enhancement factor, a more accurate mass flux can be recovered, suggesting that joint inversions for basal friction and the isotropic flow-rate factor may be able to compensate for mechanical anisotropies caused by the fabric. Thus, in addition to other sources of rheological uncertainty, fabric might complicate attempts to relate subglacial conditions to basal properties inferred from an inversion relying on Glen's law.

Bulk directional enhancement factors are determined for axisymmetric (girdle and single-maximum) orientation fabrics using a transversely isotropic grain rheology with an orientation-dependent non-linear grain fluidity. Compared to grain fluidities that are simplified as orientation independent, we find that bulk strain-rate enhancements for intermediate-to-strong axisymmetric fabrics can be up to a factor of ten larger, assuming stress homogenization over the polycrystal scale. Our work thus extends previous results based on simple basal slip (Schmid) grain rheologies to the transversely isotropic rheology, which has implications for large-scale anisotropic ice-flow modelling that relies on a transversely isotropic grain rheology. In order to derive bulk enhancement factors for arbitrary evolving fabrics, we expand the c-axis distribution in terms of a spherical harmonic series, which allows the rheology-required structure tensors through order eight to easily be calculated and provides an alternative to current structure-tensor-based modelling.

Further to systematic experiments on the flexural strength of laboratory-grown, fresh water ice loaded cyclically, this paper describes results from new experiments of the same kind on lake ice harvested in Svalbard. The experiments were conducted at −12 °C, 0.1 Hz frequency and outer-fiber stress in the range from ~ 0.1 to ~ 0.7 MPa. The results suggest that the flexural strength increases linearly with stress amplitude, similar to the behavior of laboratory-grown ice.

Drag at the bed and along the lateral margins are the primary forces resisting flow in outlet glaciers. Simultaneously inferring these parameters is challenging since basal drag and ice viscosity are coupled in the momentum balance, which governs ice flow. We test the ability of adjoint-based inverse methods to infer the slipperiness coefficient in a power-law sliding law and the flow-rate parameter in the constitutive relation for ice using a regularization scheme that includes coefficients weighted by surface strain rates. Using synthetic data with spatial variations in basal drag and ice rheology comparable to those in West Antarctic Ice Streams, we show that this approach allows for more accurate inferences. We apply this method to Bindschadler and MacAyeal Ice Streams in West Antarctica. Our results show relatively soft ice in the shear margins and spatially varying basal drag, with an increase in drag with distance upstream of the grounding line punctuated by localized areas of relatively high drag. We interpret soft ice to reflect a combination of heating through viscous dissipation and changes in the crystalline structure. These results suggest that adjoint-based inverse methods can provide inferences of basal drag and ice rheology when regularization is informed by strain rates.

Streaming ice accounts for a major fraction of global ice flux, yet we cannot yet fully explain the dominant controls on its kinematics. In this contribution, we use an anisotropic full-Stokes thermomechanical flow solver to characterize how mechanical anisotropy and temperature distribution affect ice flux. For the ice stream and glacier geometries we explored, we found that the ice flux increases 1–3% per °C temperature increase in the margin. Glaciers and ice streams with crystallographic fabric oriented approximately normal to the shear plane increase by comparable amounts: an otherwise isotropic ice stream containing a concentrated transverse single maximum fabric in the margin flows 15% faster than the reference case. Fabric and temperature variations independently impact ice flux, with slightly nonlinear interactions. We find that realistic variations in temperature and crystallographic fabric both affect ice flux to similar degrees, with the exact effect a function of the local fabric and temperature distributions. Given this sensitivity, direct field-based measurements and models incorporating additional factors, such as water content and temporal evolution, are essential for explaining and predicting streaming ice dynamics.

Systematic experiments reveal that the flexural strength of freshwater S2 columnar-grained ice loaded normal to the columns increases upon cyclic loading. Specifically, over the range of stress amplitudes 0.1–2.6 MPa the flexural strength increases linearly with increasing stress amplitude. The experiments were conducted upon both reversed and non-reversed cyclic loading over ranges of frequencies from 0.03 to 2 Hz and temperatures from −25 to −3°C. Strengthening can also be imparted through bending-induced creep. The fundamental requirement for strengthening is that the surface that undergoes maximum tensile stress during failure must have been pre-stressed in tension. Flexural strength is governed by crack nucleation. We suggest that the process is resisted by an internal back-stress that opposes the applied stress and builds up through either crystal dislocations piling up or grain boundaries sliding.

Hydrofracturing can enhance the depth to which crevasses propagate and, in some cases, allow full depth crevasse penetration and iceberg detachment. However, many existing crevasse models either do not fully account for the stress field driving the hydrofracture process and/or treat glacier ice as elastic, neglecting the non-linear viscous rheology. Here, we present a non-local continuum poro-damage mechanics (CPDM) model for hydrofracturing and implement it within a full Stokes finite element formulation. We use the CPDM model to simulate the propagation of water-filled crevasses in idealized grounded glaciers, and compare crevasse depths predicted by this model with those from linear elastic fracture mechanics (LEFM) and zero stress models. We find that the CPDM model is in good agreement with the LEFM model for isolated crevasses and with the zero stress model for closely-spaced crevasses, until the glacier approaches buoyancy. When the glacier approaches buoyancy, we find that the CPDM model does not allow the propagation of water-filled crevasses due to the much smaller size of the tensile stress region concentrated near the crevasse tip. Our study suggests that the combination of non-linear viscous and damage processes in ice near the tip of a water-filled crevasse can alter calving outcomes.

This work quantifies the increased temperature sensitivity of the constitutive behavior of ice with proximity to the melting point in terms of dislocation mechanics. An analysis of quasistatic and dynamic cyclic loading data for several ice types leads to the conclusion that high temperature (e.g. T ≥ −8°C) behavior is the result of a thermally induced increase in the number of mobile dislocations rather than an increase in the activation energy of dislocation glide or the introduction of a new deformation mechanism. The relationship between dislocation density and temperature is quantified and the model is shown to adequately represent the published minimum creep rate vs stress data for isotropic granular freshwater ice for −48 ≤ T ≤ −0.01°C.

Basal ice of glaciers and ice sheets frequently contains a well-developed stratification of distinct, semi-continuous, alternating layers of debris-poor and debris-rich ice. Here, the nature and distribution of shear within stratified basal ice are assessed through the anisotropy of magnetic susceptibility (AMS) of samples collected from Matanuska Glacier, Alaska. Generally, the AMS reveals consistent moderate-to-strong fabrics reflecting simple shear in the direction of ice flow; however, AMS is also dependent upon debris content and morphology. While sample anisotropy is statistically similar throughout the sampled section, debris-rich basal ice composed of semi-continuous mm-scale layers (the stratified facies) possesses well-defined triaxial to oblate fabrics reflecting shear in the direction of ice flow, whereas debris-poor ice containing mm-scale star-shaped silt aggregates (the suspended facies) possesses nearly isotropic fabrics. Thus, deformation within the stratified basal ice appears concentrated in debris-rich layers, likely the result of decreased crystal size and greater availability of unfrozen water associated with high debris content. These results suggest that variations in debris-content over small spatial scales influence ice rheology and deformation in the basal zone.

Experimental data from creep tests on polycrystalline ice samples highlight not only the non-Newtonian behavior of ice but also suggest a critical dependence of the various rheological parameters upon the applied hydrostatic pressure. We propose a new modeling framework, based on implicit theories of continuum mechanics, that generalizes two well-known constitutive models by taking into account the effect of the pressure in the description of ice in creep. To ascertain the validity of the proposed models, we fit the physical parameters with experimental data for the elongational flow of ice samples. The results show good agreement with the experimental creep curves. In particular, the proposed generalized models reproduce the increase of the creep rate due to the presence of hydrostatic pressure.

Over a year of seismic observations, ~5000 short duration icequakes were detected by a permanent broadband station installed at the Princess Elisabeth base, located ~180 km inland in eastern Dronning Maud Land, East-Antarctica. Icequake detection via seismic waveform pattern recognition indicates the presence of two dominating clusters of events, totalizing ~1500 icequakes. The corresponding icequake locations point towards two distinct zones of outcropping blue ice areas (BIAs) located respectively at 4 and 1 km from the seismic station, both on the leeward side of a nunatak protruding through the ice sheet. The temporal occurrence of these icequakes suggests a close genetic link with thermal contraction of ice caused by significant surface cooling controlled, in summer by variations in diurnal solar radiation and in winter by strong cooling during cold katabatic regimes. Further analysis demonstrates the dependence of these icequakes on the absolute surface temperature and on its temporal change. Besides providing information on the ice fracture mechanics and rheology, investigations of thermal icequakes may be regarded as a ground-based proxy for the monitoring of the thermal state of BIAs, and characterization of ice-sheet ablation zones.

This contribution discusses results obtained from 3-D neutron diffraction and 2-D fabric analyser in situ deformation experiments on laboratory-prepared polycrystalline deuterated ice and ice containing a second phase. The two-phase samples used in the experiments are composed of an ice matrix with (1) air bubbles, (2) rigid, rhombohedral-shaped calcite and (3) rheologically soft, platy graphite. Samples were tested at 10°C below the melting point of deuterated ice at ambient pressures, and two strain rates of 1 × 10−5 s−1 (fast) and 2.5 × 10−6 s−1 (medium). Nature and distribution of the second phase controlled the rheological behaviour of the ice by pinning grain boundary migration. Peak stresses increased with the presence of second-phase particles and during fast strain rate cycles. Ice-only samples exhibit well-developed crystallographic preferred orientations (CPOs) and dynamically recrystallized microstructures, typifying deformation via dislocation creep, where the CPO intensity is influenced in part by the strain rate. CPOs are accompanied by a concentration of [c]-axes in cones about the compression axis, coinciding with increasing activity of prismatic-<a> slip activity. Ice with second phases, deformed in a relatively slower strain rate regime, exhibit greater grain boundary migration and stronger CPO intensities than samples deformed at higher strain rates or strain rate cycles.

Ice rheology governs how glaciers flow and respond to environmental change. The rheology of glacier ice evolves in response to a variety of mechanisms, including damage, heating, melting and the development of crystalline fabric. The relative contributions of these rheological mechanisms are not well understood. Using remotely sensed data and physical models, we decouple the influence of each of the aforementioned mechanisms along the margins of Rutford Ice Stream, a laterally confined outlet glacier in West Antarctica. We show that fabric is an important control on ice rheology in the shear margins, with an inferred softening effect consistent with a single-maximum fabric. Fabric evolves to steady state near the onset of streaming flow, and ice progressively softens downstream almost exclusively due to shear heating. The rate of heating is sensitive to local shear strain rates, which respond to local changes in bed topography as ice is squeezed through the basal trough. The impact of shear heating on the downstream evolution of ice rheology in a laterally confined glacier suggests that the thermoviscous feedback – wherein faster ice flow leads to higher rates of shear heating, further softening the ice – is a fundamental control on glacier dynamics.

Tidal flexure in ice shelf grounding zones has been used extensively in the past to determine grounding line position and ice properties. Although the rheology of ice is viscoelastic at tidal loading frequencies, most modelling studies have assumed some form of linear elastic beam approximation to match observed flexure profiles. Here we use density, radar and DInSAR measurements in combination with full-Stokes viscoelastic modelling to investigate a range of additional controls on the flexure of the Southern McMurdo Ice Shelf. We find that inclusion of observed basal crevasses and density dependent ice stiffness can greatly alter the flexure profile and yet fitting a simple elastic beam model to that profile will still produce an excellent fit. Estimates of the effective Young's modulus derived by fitting flexure profiles are shown to vary by over 200% depending on whether these factors are included, even when the local thickness is well constrained. Conversely, estimates of the grounding line position are relatively insensitive to these considerations for the case of a steep bed slope in our study region. By fitting tidal amplitudes only, and ignoring phase information, elastic beam theory can provide a good fit to observations in a wide variety of situations. This should, however, not be taken as an indication that the underlying rheological assumptions are correct.

More than 170 years ago, Louis Agassiz, one of the creators of glacial theory, made his first attempt to drill into the bed of Unteraargletscher, Swiss Alps. Since that time, various systems for thermal and mechanical drilling have been designed especially for boring into ice, and some conventional drill rigs been adopted for ice coring. Although contemporary ice-drilling knowledge and techniques are now familiar, there remain many problems to be solved by advanced modern technology. Specific challenges related to improving old drilling methods and developing new emerging technologies include: (1) identification of depth limitation of ‘dry’ drilling; (2) improvement of casing; (3) searching for the new environmentally friendly low-temperature drilling fluids; (4) reliable elimination of sticking drills; (5) improvement of core quality in the brittle zone; (6) additional core sampling from borehole walls after the core has been drilled; (7) obtaining oriented core; (8) designing automation drilling systems; (9) developing rapid-access drills. Possible ways of solving these problems are presented below.

Marine ice is an important component of ice shelves in Antarctica. It accretes in substantial amounts at weak points and below ice shelves. It is likely to exhibit peculiar rheological properties, which are crucial to understanding its potential role in stabilizing ice-shelf flow. Due to its location and consolidation processes, marine ice can present a variety of textures which are likely to influence its rheological properties. We present a new dataset of unconfined uniaxial compression experiments on folded marine ice samples that have been cut at various angles to the folds. Texture and fabric analyses are described ‘before’ and ‘after’ the deformation experiment. It is shown that, in the given stress configuration, the geometry of the anisotropy controls the rheological behaviour of the marine ice. During secondary creep, folded marine ice is harder to deform than weakly textured ice when compressed parallel or perpendicular to the folds' hinges, while the reverse is true for ice compressed at 45°. The observed range of values for the n exponent in Glen's flow law is between 2.1 and 4.1. Surprisingly, we see that tertiary creep tends to develop at a higher total strain than for randomly oriented impurity-free meteoric ice.